Samantha aka Sam of Totally Spies!. The first OP has her expertly using a chemistry kit as Clover and Alex watch her in amazement. While at the same time, she is able to fight off the random villains that the trio encounter just as effectively as her partners. AND she also manages to get and keep excellent grades at school.
As if that wasn't enough, the spinoff The Amazing Spiez brings us Marc, who's essentially a younger male version of Sam. This is lampshaded in "Operation Killer Condos" when the Spiez use one of their gadgets to disguise as the original spies (and Jerry), and Marc-as-Sam points out that he gets to be the smart one.
Steven Universe's Pearl is a pretty good example of this trope. She enjoys domestic things like baking and cleaning, willingly took up the entire chore wheel, and acts like a mother towards Steven. The episode Last One Out of Beach Cityblatantly labels her as "Repressed Nerd". Despite all this, she's also a highly trained samurai and assassin, gifted technician, and was known during the Gem War as the "Terrifying Renegade Pearl".
This gets even more badass after the revelation in the episode Back to the Barn. Peridot reveals that Pearls are created to be servants, and that their only purpose is "standing around, looking nice and holding your stuff for you". This means that all of the things mentioned above are not naturally in Pearl's skillset, which is the case with Amethyst, Jasper, Garnet (kind of) and Peridot. She learned all of that from scratch. She knows her strengths and weaknesses, and while she's physically not as strong as the other gems, she's very fast and incredibly agile. She usually uses that to her advantage to outsmart her enemies.
One of the few exceptions to this rule is in the same episode mentioned above. Peridot had been teasing Pearl for being a servant and not doing what she was designed to do for the entire episode. When Pearl finally gets enough, she gives Peridot a hell of a right hook.
While Justice League member The Question is more crackpot than bookworm, he does distill this trope into one glorious moment where he nails a guy in the face with a computer monitor just after he's finished using it. He needs to be near threatened by his girlfriend to take her out, rather than review newly taken information from enemies.
Raven from Teen Titans is very reserved, and spends a lot of her time reading but anyone who seriously pisses her off will have their ass handed to them. Just ask Dr. Light (see the episode "Nevermore.")
In Challenge of the Super Friends, Asian Captain Ethnic Samurai (real name: Toshio Etou) was actually a Japanese history professor in the University of Tokyo before he was turned into a super hero by the New Gods of New Genesis.
In Jonny Quest: The Real Adventures, scientist Benton Quest sometimes shows badass tendencies (though he's usually overshadowed by his more conventionally badass bodyguard, Race Bannon), particularly during his escape from the villain's headquarters in "General Winter" and his climactic fight with Big Bad Dr. Zin in "The Robot Spies." This was also true in the original Jonny Quest series, in which Dr. Quest is a "real dynamo when he gets going" according to Race Bannon himself.
Jessie and Hadji are no slouches either since they've saved each other and Jonny multiple times.
In Spiral Zone, Benjamin Davis Franklin of the Zone Riders is a geeky, scrawny sciene nerd who looks like "Weird Al" Yankovic. Nevertheless, he's tough enough to kick Big Bad Overlord in the face in one episode.
Danny's brainy older sister Jazz in Danny Phantom discovers she has amazing ghost fighting skills in "Maternal Instincts". She has since displayed said skills in a couple of other episodes. We're going to ignore "Secret Weapons".
Dexter, from Dexter's Laboratory, is a tiny, stub-limbed boy genius who spends all his time in his secret laboratory, trying — in vain — to keep his pretty-princess Cloudcuckoolander sister out. Until a monster attacks the city, or aliens invade, or a meteor threatens Earth; then Dexter pulls out one of his giant, anime-inspired robots, super-powered exoskeleton suits, or space ships and kicks ass. He also seems to have learned kung-fu at some point.
Blossom from The Powerpuff Girls. Professor Utonium himself became one in "Powerprof", when he builds a suit that gives him powers.
Starscream was a Cybertronian scientist before his ascension to air commander of the Decepticon forces.
There's also Wheeljack, the cheerful crazy inventor, who can hold his own in battle quite well.
To an extent, Kyle from South Park. On the outside, a potty-mouth, angry nine-year old who's also the smart one of the group, but the movie demonstrated that he can hack into top secret military databases. He has also been shown to be fairly athletic at points of the show and fully capable of kicking Cartman's ass when necessary.
First is the obvious one, Lexington. Though the smallest of the clan, he maintains incredible strength (like bending metal spikes). What's more, ever since waking up to a technologically advanced society, he's engrossed himself in it. He built a motorcycle and flew a chopper.
David Xanatos. He's well-spoken, a keen businessman with several hundred million to his name, an avid chess-player, and indulged his geeky side by quoting the film version of Frankenstein (1931), admitting I Always Wanted to Say That. As for the badass portion of the equation? He's a black-belt who beats up gargoyles and other mythological creatures with Power Armor, which he invented.
If the Canterlot Wedding episode is any indication, Twilight had decided to dig into the books on offensive magic at some point along the way. She can shoot lasers from her horn; Pinkie Pie even uses her as a machine-gun.
In the season 4 finale this get turned to 11 when Big Bad Tirek sucks all the magic out of Equestria and then comes after her. She tries to flee from him so that he won't get her magic too, but then when he blows up the library she'd lived in since arriving in Ponyville she wordlessly turns on a dime and engages him in a mountain-shattering battle worthy of Dragon Ball Z.
In the season 7 finale, she proves her bookworm badassery to her precursor Star Swirl the Bearded (whose unfinished spell about Cutie Mark magic she had finished in the season 3 finale, for which she earned her Princess crown) by developing a spell that would banish The Pony of Shadows without sacrificing anypony else in the process.
Huey Freeman from The Boondocks is probably the most intelligent character of the series, and is often seen reading or watching the news to heighten his awareness. He is also one of the best fighters of the series, and his kung fu skills are something to watch out for from this 10-year-old boy.
Archer, episode "The Rock": Stuck in the laundromat below the ISIS facilities, a couple of the nerdy "drones" employed by ISIS build a GPS-enabled communication device out of cell phones, a cash register, lasers, wires, a belt, paper clips, and the mica crystal of an engagement ring, with which they use to call a helicopter to save Archer and Lana in San Morino. Even Pam is impressed:
Pam: Holy shit, you geeks are badass.
As if that wasn't enough, Krieger doesn't activate this makeshift communicator — one that could save Archer and Lana from certain death — until Malory Archer guarantees him and his coworkers a pay raise.
Cyril, of all people, gets to be one of these during "El Contador" He manages to bluff his way into a Colombian drug lord's compound using only his dossiers and Calzado's greed, then devises the plan to catch Calzado. Even Lana is impressed.
Ferb. At the end of an episode that revolved around Phineas training to beat Buford, Ferb knocked the bully out with one pinch. ("Well, he was all up in my face.") He also tends to get the "action"-type sequences in general, being "more of a man of action" than a talker, and he can build anything. And yet, if it weren't for Phineas he'd probably just be sitting under that tree, reading a book all summer...
Dipper Pines may not be very athletic, but he's still got enough nerve and cunning to take on the supernatural weirdness he finds in his investigations.
The Author is the very definition of this trope. He wrote the series of Journals that told of many of the anomalies and dangers in Gravity Falls, many of which are very dangerous— including Bill Cipher. He invented a transdimensional portal, and when he was sucked into it, he survived for 30 years on the other side. He's very physically fit despite being in his 60s. He's also a certifiable genius, with 12 doctorate degrees.
It's no surprise these two get along very well when they finally meet in the second half of season 2.
Amon, the Big Bad from The Legend of Korra, is a very agile fighter who is perfectly willing to fight benders along with his followers and is also an incredibly charismatic public speaker and utterly brilliant Chessmaster.
Similarly, Asami is (scientifically speaking) either the smartest or second smartest person in the world, and a good enough hand-to-hand fighter to take on Equalists and powerful benders alike.
Adventure Time: Princess Bubblegum. Also, Simon Petrikov aka the original identity of the Ice King, who manages to survive in the radioactive ruins for years while protecting little Marceline and fighting the crown's influence.
In Motorcity, Dutch turns out to be this in "Going Dutch" in which he's the only one able to fight off a Zombie Apocalypse and then again in "Vega" when he has to lead the Burners after Mike has been captured. While usually averted with Chuck, in "Fearless" he does manage to stand up to his fears and uses his brains to turn off the KMG after he has to "fly" to it.
The title character in the Pakistani show Burka Avenger- a schoolteacher who literally uses books and pens as weapons in the In-Universe martial art Takht Kabaddi to protect access to education and women's rights.